from manim import *



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(60*2+1):       
            dot1=Dot([-500,5*(i-60),0]).set_opacity(0.5)
            dot2=Dot([500,5*(i-60),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(100*2+1):        
            dot3=Dot([(i-100)*5,-300,0]).set_opacity(0.5)
            dot4=Dot([(i-100)*5,300,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        self.play(self.camera.frame.animate.scale(1).move_to([0,0,0]))
        
        #题目出现
        text = Tex(r"\text{(张1000)若函数}$f\left( x\right) $\text{满足关系式}$f^{'}\left( x\right) +af\left( x\right) =\int _{x}^{0}f\left( t\right) dt,$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,23,0])
        text0 = Tex(r"$a >0,$\text{求}$\int _{0}^{+\infty }f\left( x\right) dx$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,19,0])
        





        
        self.play(Create(text),Create(text0))
        self.wait(0.2)
       
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
       
        text2 = Tex(r"\text{微分方程+积分}",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([0,0,0])
        self.play(Create(text2))
        text3 = Tex(r"\text{特征}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([0,0,0])
        self.play(
            
            ReplacementTransform(text2,text3)
            
        )
        text4 = Tex(r"\text{特定思路}",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([0,0,0])
        self.play(
            
            ReplacementTransform(text3,text4)
            
        )
        text5 = Tex(r"\text{将积分问题转化为极限问题}",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([0,0,0])
        self.play(
            
            ReplacementTransform(text4,text5)
            
        )
        rectangle=Rectangle(color=BLUE,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([20,23,0])
        self.play(
            rectangle.animate.stretch(31.0,dim=0)
        )
        text6 = Tex(r"$f'\left( +\infty \right) +af\left( +\infty \right) =\int _{+\infty }^{0}f\left( x\right) dx$",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-25,5,0])
        self.play(
            
            ReplacementTransform(text5,text6),
            ReplacementTransform(rectangle,text6),
        )
        rectangle=Rectangle(color=BLUE,fill_opacity=0.0,width=12,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle.move_to([30, 23, 0])
        self.play(Create(rectangle))
        self.play(FadeOut(rectangle))
        rectangle=Rectangle(color=BLUE,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([20,23,0])
        self.play(
            rectangle.animate.stretch(31.0,dim=0)
        )
        text7 = Tex(r"$f''\left( x\right) +af'\left( x\right) +f\left( x\right) =0$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,13,0])
        self.play(
            
            
            ReplacementTransform(rectangle,text7),
        )
        text8 = Tex(r"$\lambda ^{2}+a\lambda +1=0$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,10,0])
        self.play(Create(text8))
        text9 = Tex(r"$\Rightarrow \Delta =a^{2}-4$\text{有3种情况}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,5,0])
        self.play(Create(text9))
        text10 = Tex(r"$\lambda _{1}+\lambda _{2}=-a <0$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,0,0])
        text100 = Tex(r"$\Rightarrow $",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([5,-1.5,0])
        text11 = Tex(r"$\lambda _{1}\lambda _{2}=1 >0$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,-3,0])
        self.play(Create(text10),Create(text11),Create(text100))

        text12 = Tex(r"$\Rightarrow \lambda _{1},\lambda _{2} <0$",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,-8,0])
        self.play(Create(text12))

        text13 = Tex(r"$0$",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-40,0,0])
        text14 = Tex(r"$0$",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-26,0,0])
        self.play(Create(text13),Create(text14))
        text15 = Tex(r"$0$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-15,0,0])
        self.play(Create(text15))
        self.wait()